Integral Calculator

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint and idempotentHint, confirming no side effects. The description goes beyond by detailing behavioral traits: it distinguishes symbolic (exact) vs numerical (approximate), notes that numerical requires bounds, and shows result formats (e.g., returning an expression or a number). This fully clarifies behavior.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is fairly concise given the complexity; it front-loads the purpose and uses bullet-like examples. However, the examples are somewhat lengthy and could be condensed without losing clarity. Still, every sentence adds value, and the structure is logical.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the tool's complexity (7 parameters, 2 required, with enums and optional bounds), the description is complete. The output schema exists but is not shown; the description compensates with example outputs. All parameter interactions are clarified, and edge cases (e.g., non-elementary integrals) are covered.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Despite 100% schema coverage, the description adds significant value through examples showing how each parameter is used (e.g., expression='x^2', variable='x', lower_bound=0, upper_bound=1, method='numerical'). The examples clarify the meaning of bounds and method, and even show the context parameter used implicitly? Actually context is not shown, but the rest is well illustrated.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description starts with a clear verb+resource: 'Compute symbolic and numerical integrals (definite and indefinite).' It provides many examples covering indefinite, definite, trigonometric, numerical, and symbolic cases, which distinctly sets it apart from sibling tools like derivative or limits_series.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description includes extensive examples that implicitly show when to use integrals (e.g., symbolic vs numerical), but it lacks explicit guidance on when to prefer this tool over alternatives or when not to use it. No exclusions or prerequisites are mentioned, which is a gap for an AI agent deciding between tools.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.